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{ COMPLEX+TIME.PDE
This example shows the use of complex variables in time-dependent systems.
The equation that is solved is not intended to represent any real application.
}
title 'Complex transient equations'
Variables
U(0.01) = complex (Ur,Ui) { creates variables Ur and Ui }
definitions
u0 = 1-x^2-y^2
s = complex(4,x)
equations
{ create two scalar equations, one for Ur and one for Ui }
U: del2(U) +s = dt(U)
boundaries
Region 1
start(-1,-1)
natural(Ur)=u0-Ur
line to (1,-1) to (1,1) to (-1,1) to close
time 0 to 1
plots
for cycle=10
contour(Ur,Ui)
contour(Real(u),Imag(U))
contour(U)
vector(U)
elevation(u,s) from(-1,0) to (1,0)
history(u,s) at (0,0)
end